Adaptive compensation circuitry for suppression of distortions generated by the dispersion-slope of optical components

ABSTRACT

A distortion compensation circuit compensates for the distortions generated by the dispersion-slope of an optical component and the frequency chirp of an optical transmitter. The dispersion compensation circuitry can be utilized in the optical transmitter, the optical receiver and/or at some intermediate point in a fiber-optic network. One embodiment of the compensation circuit utilizes a primary electrical signal path that receives at least a portion of the input signal and a delay line; and a secondary signal path in parallel to the primary path that receives at least a portion of the input signal and including: an amplifier with an electrical current gain that is proportional to the dispersion-slope of the optical component, an optional RF attenuator, an optional delay line, a “squarer” circuit, and a “differentiator” circuit. Another embodiment of the disclosure performs simultaneous, and independent, compensation of second-order distortions generated by both the dispersion-slope of a first optical component and the dispersion of a second optical component. Other embodiments of the disclosure perform adaptive predistortion for compensation of distortions generated by the dispersion-slope of a first optical component and the dispersion of a second optical component to maintain optimum compensation even if the dispersion properties of the optical components change with time.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of, and claims a benefit of priorityunder 35 U.S.C. 120 from utility patent application U.S. Ser. No.14/302,339, filed Jun. 11, 2014 (now U.S. Pat. No. 9,160,457, issuedOct. 13, 2015), which in-turn claims a benefit of priority under35U.S.C. 119(e) from provisional patent application U.S. Ser. No.61/834,410, filed Jun. 12, 2013 the entire contents of both of which arehereby expressly incorporated herein by reference for all purposes.

BACKGROUND INFORMATION

Transmission of directly modulated lasers (or other light sources)through optical components results in generation of second-orderdistortion due to the chromatic dispersion properties of the opticalcomponents and chirp (i.e., wavelength variations) of the laser (orother light source). Within this application the term optical componentsis used to denote optical devices that exhibits chromatic dispersion,meaning that the time delay of the signal through the device varies withthe optical wavelength. This includes, but is not limited to, bothpassive components such as optical fiber, optical filters, multiplexers,waveguides, etc. and also active optical components such as opticalamplifiers (e.g., EDFAs, Raman amplifiers), modulators, integrateddevices, etc.

The composite second-order (CSO) distortion is an indication of theseverity of these second-order distortions. CSO distortion due to thechromatic dispersion properties of optical components degrade theperformance of continuous-wave (CW) analog signals and pseudo-analogsignals such as quadrature-amplitude modulated (QAM) signals.

FIG. 1A illustrates a fiber-optic system including a conventionaldirectly modulated laser whose optical output goes through an opticalcomponent and is then detected by the optical receiver Rx. The opticaloutput of the laser is directly modulated by a current signal I(t) whichcontains the signal information. The light from the laser goes throughthe optical component, and the optical output of the component isdenoted by P_(OUT)(t). The photodiode current in the receiver is denotedby I_(PD)(t).

The optical component is treated as a linear transmission element thatis described by two parameters: optical attenuation α and delay τ. Thechromatic dispersion of the optical component results in the delay beinga function of wavelength; that is, τ=τ.(λ). The combined effects ofchromatic dispersion and laser chirp is to delay different parts of theinput waveforms by different amounts, which results in an amplitudecorrection factor of [1+t,?∂τ/∂t]⁻¹ that causes distortion of the inputoptical waveform. Consequently, the output of the optical component isgiven by the equation:

$\begin{matrix}{{P_{OUT}(t)} = \frac{\alpha\;{P_{IN}\left( {t - {\tau(\lambda)}} \right)}}{\left\lbrack {1 + \frac{\partial\tau}{\partial t}} \right\rbrack}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$as shown in FIG. 1A.Dispersion Compensation Techniques

Several strategies are known to those skilled in the art to avoid orsuppress such second-order distortions. One is to tune the wavelength ofthe laser to the zero-dispersion wavelength of the optical component.The CSO distortion that is generated by the dispersion of the opticalcomponent then becomes negligible.

However, sometimes it is not possible to tune the laser wavelength tothe zero-dispersion wavelength of the optical component. For example, ifthe laser transmitters are used in a DWDM system, then the laserwavelengths are constrained to specific values defined by standardgroups such as the ITU and cannot be arbitrarily tuned. An example is aDWDM system operating in the C-Band (1550 nm region) of conventionalsingle-mode fiber, the zero-dispersion wavelength is near 1310 nm andtherefore the laser wavelengths cannot be tuned to the zero-dispersionwavelength of the optical fiber. In this case, the dispersion of theoptical component (the optical fiber in this instance) is unavoidablyhigh.

In those systems where the dispersion of the optical component is high,other techniques to suppress second-order distortions are known to thoseskilled in the art. There are several inventions that describe laserpredistortion circuits to compensate for the second-order distortionsgenerated by dispersion.

Dispersion-Slope Compensation Techniques

There are cases where the optical components also have extremely highvalues of dispersion-slope. “Dispersion-slope” refers to the slope ofthe dispersion characteristic of the optical components when plotted asa function of the optical wavelength. For example, dispersion slopes ashigh as 150 ps/nm² have been measured in optical filters used in DWDMsystems. In comparison, 20 km of conventional single-mode fiber has adispersion slope at the zero-dispersion wavelength of less than 2ps/nm².

That is, the dispersion-slope of some optical components can be as highas that of 1600 km of optical fiber. At these high values of dispersionslopes, second-order effects (modulation of fiber delay due to residualdispersion that arises from the second-order term in the power seriesexpansion of the delay characteristic) generates significant CSOdistortion that can degrade the performance of CATV systems that employanalog signals or quasi-analog signals such as QAM.

It has been found that the dispersion-slope-induced CSO distortion canbe as severe in magnitude as the CSO generated by the dispersion of theoptical components at high dispersion-slope values. That is,second-order distortions can be generated both by the dispersion anddispersion-slope of optical components. This disclosure is concernedwith suppressing the distortions generated by the dispersion-slope ofoptical components.

Prior inventions that describe suppression of second-order distortionsgenerated by the dispersion of the optical components do not apply tothe suppression of CSO generated by the dispersion-slope of the opticalcomponents. There are other inventions, however, that deal withsuppression of CSO distortions generated by the dispersion-slope ofoptical components. They are generally referred to as dispersion-slopecompensation techniques.

These prior dispersion-slope compensation inventions generally involveadding another device (or fiber) after the laser transmitter that has adispersion-slope opposite in sign and equal in magnitude to thedispersion-slope of the optical component whose distortions you aretrying to suppress. These other inventions suffer from two majordisadvantages compared to the instant disclosure: (1) They usuallycompensate for only one value of dispersion-slope. Therefore, thedispersion-slope compensation device has to be tailor-made for theoptical component whose distortions you are trying to suppress. If theoptical component is replaced then the compensation device also has tobe replaced. (2) The dispersion-slope compensation device is usuallyexpensive—often as expensive, or more expensive, than the opticalcomponent whose distortion one is trying to suppress.

The present disclosure overcomes these limitations of previousinventions by performing dispersion-slope compensation using electroniccompensation circuitry rather than using optical devices that have adispersion slope opposite in sign to the component whosedispersion-slope one is trying to compensate. The compensation circuitryis also sometimes referred to as predistortion circuitry, but this mustnot be construed as limiting the location of this circuitry to a pointprior to the optical source, such as in the optical transmitter. Sincethe generation of CSO distortion due to the dispersion anddispersion-slope of optical components is a linear process, thecompensation circuitry can be placed anywhere in the opticalnetwork—either in the optical transmitter prior to the light source orin the optical receiver after the optical photodiode.

The cost of the electronic compensation circuitry describe in thisdisclosure is negligible since the technique adds a few inexpensiveelectronic parts to the existing optical transmitter or receiver.Furthermore, the compensation circuitry of this disclosure cancompensate for the distortion generated by any value ofdispersion-slope, and could even be made adaptive so that the techniqueremains effective even if the dispersion-slope of the optical componentchanges over time—and is therefore superior to prior inventions.

SUMMARY

There is a need for the following embodiments of the disclosure. Ofcourse, the disclosure is not limited to these embodiments.

According to an embodiment of the disclosure, a process comprises:modulating the drive current of a laser via a direct path including adelay line and a parallel secondary path including a squarer,differentiator, and an amplifier that provides a gain proportional tothe dispersion-slope of an optical component.

According to another embodiment of the disclosure, laser drive circuitryincludes a direct path containing a delay line, a first parallel pathincluding a squarer, differentiator, delay line, and an amplifier thatprovides a gain proportional to the dispersion of a first opticalcomponent, and a second parallel path including a squarer,differentiator, and an amplifier that provides a gain proportional tothe dispersion-slope of a second optical component. This embodimentprovides for the simultaneous, and independent, compensation for CSOdistortion generated by the dispersion of one optical component and alsofor the CSO distortion generated by the dispersion-slope of a secondoptical component.

In another embodiment of this disclosure, the compensation circuitry isplaced after the optical receiver. In this embodiment of the disclosure,the photodiode current output of the optical receiver is split into adirect path including a delay line and a parallel secondary pathincluding a squarer, differentiator, and an amplifier that provides again proportional to the dispersion-slope of an optical component.

In other embodiments of this disclosure, the amplifier in the secondarypath, whose gain is nominally set to a value proportional to thedispersion-slope of the optical component, is replaced by avoltage-controlled-amplifier whose gain can be adjusted by an errorvoltage. The error voltage is obtained by feeding a small part of theoutput of the optical component to a photodiode and then using aband-pass filter that is tuned to a frequency where there is an unwantedsecond-order distortion present. In this manner, this embodiment of thedisclosure uses adaptive predistortion to automatically adjust theamplifier gain to obtain the best degree of CSO suppression even if thedispersion properties of the optical component changes with time.

These, and other, embodiments of the disclosure will be betterappreciated and understood when considered in conjunction with thefollowing description and the accompanying drawings. It should beunderstood, however, that the following description, while indicatingvarious embodiments of the disclosure and numerous specific detailsthereof, is given for the purpose of illustration and does not implylimitation. Many substitutions, modifications, additions and/orrearrangements may be made within the scope of an embodiment of thedisclosure without departing from the spirit thereof, and embodiments ofthe disclosure include all such substitutions, modifications, additionsand/or rearrangements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a fiber-optic system including a conventionaldirectly modulated laser Tx whose optical output goes through an opticalcomponent and is then detected by an optical receiver Rx, appropriatelylabeled prior art.

FIG. 1B is a schematic diagram of a fiber-optic system includingpredistortion circuitry in an optical transmitter.

FIG. 1C is a schematic diagram of a fiber-optic system includingcompensation circuitry in an optical receiver.

FIG. 2 is an embodiment of the disclosure illustrating a predistortioncircuit that compensates for the CSO distortion generated by thedispersion-slope of an optical component.

FIG. 3 is another embodiment of the disclosure where an adaptivepredistortion path is added to the predistortion circuit that fine-tunesthe gain of a voltage-controlled amplifier so that maximum suppressionof CSO distortion is automatically obtained, even if laser or opticalcomponent parameters change with time.

FIG. 4 is another embodiment of the disclosure where an adaptivepredistortion path is added to the predistortion circuit that fine-tunesthe gain of a voltage-controlled attenuator so that maximum suppressionof CSO distortion is automatically obtained, even if laser or opticalcomponent parameters change with time.

FIG. 5 shows the model of a system comprised of a laser, a first opticalcomponent that generates CSO distortion due to its dispersion-slope, anda second optical component that generates additional CSO distortion dueto its dispersion.

FIG. 6 is an embodiment of the disclosure that provides simultaneous,and independent, compensation of both dispersion-slope induced CSOdistortion of a first optical component and dispersion-induced CSOdistortion of a second optical component using two predistortion paths.

FIG. 7 is an embodiment of the disclosure that provides simultaneous,and independent, compensation of both dispersion-slope induced CSOdistortion of a first optical component and dispersion-induced CSOdistortion of a second optical component using a single predistortionpath.

FIG. 8 shows a different method of obtaining the predistortion currentd(I²)/dt using a differentiator and a multiplier circuit rather than asquarer and differentiator.

FIG. 9 is an embodiment of the disclosure that provides simultaneous,and independent, compensation of both dispersion-slope induced CSOdistortion of a first optical component and dispersion-induced CSOdistortion of a second optical component using compensation circuitrylocated in the optical receiver.

DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the disclosure and the various features and advantageousdetails thereof are explained more fully with reference to thenon-limiting embodiments that are illustrated in the accompanyingdrawings and detailed in the following description. Descriptions of wellknown starting materials, processing techniques, components andequipment are omitted so as not to unnecessarily obscure the embodimentsof the disclosure in detail. It should be understood, however, that thedetailed description and the specific examples, while indicatingpreferred embodiments of the disclosure, are given by way ofillustration only and not by way of limitation.

The below-referenced U.S. Patent Applications disclose embodiments thatare useful for the purposes for which they are intended. The entirecontents of Patent Cooperation Treaty Publication WO/2002/089363 arehereby expressly incorporated by reference herein for all purposes. Theentire contents of U.S. Pat. App. Pub. 2009/0196629 are hereby expresslyincorporated by reference herein for all purposes.

Embodiments of the instant disclosure relate generally to the field oftransport of CATV and digital signals over an optical network. Moreparticularly, an embodiment of this disclosure relates to transport ofCATV and digital signals over optical components, both passive (opticalfilters, optical fiber, etc.) and active (optical amplifiers, EDFAs,Raman amplifiers, etc.), that exhibit high dispersion-slopes and therebygenerate significant levels of second-order distortion.

The CSO distortion at the output of the receiver generated by thedispersion-slope of the optical component can be cancelled usingcompensation circuitry including a parallel combination of is the inputsignal I(t) and a secondary path where a predistortion signalI_(predis)(t) is generated described by the equation:

$\begin{matrix}{I_{predis} = {G_{opt}\frac{\mathbb{d}\left( I^{2} \right)}{\mathbb{d}t}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$where G_(opt) is a parameter independent of I(t) and is proportional tothe dispersion slope S_(opt) of the optical component (e.g. opticalfilter) and is given by the equation:

$\begin{matrix}{G_{opt} = {\left( \frac{P_{0}S_{opt}}{S_{las}} \right)\left( \frac{\lambda^{4}}{2\; c^{2}} \right)\eta_{FM}^{2}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$In equation (3), λ denotes the wavelength of the optical signal, cdenotes the speed of light in a vacuum, η_(FM) denotes the laser chirp(also known as the laser FM efficiency) in units of MHz/mA, P₀ is theaverage power output of the laser in mW, S_(las) denotes the slope ofthe laser light-current characteristic in units of mW/mA, and S_(opt)denotes the dispersion-slope of the optical component in units of ps/nm²at wavelength λ. The compensation circuitry is typically incorporatedinto the optical transmitter, but it can also be incorporated into theoptical receiver circuitry, if desired.

In summary, compensation of the distortions is performed by generationof a predistortion current that is applied in parallel with the inputsignal current I(t). This predistortion current is advantageouslyproportional to the time derivative of the square of the signal currentI(t) and is advantageously amplified by an amplifier with a current gainthat is proportional to the dispersion-slope S_(opt) of the opticalcomponent. FIG. 1B shows a fiber-optic system including predistortioncircuitry 105 in (or coupled to) the optical transmitter 110. FIG. 1Cshows a fiber-optic system including (predistortion) compensationcircuitry 115 in (or coupled to) the optical receiver 120. An embodimentof this disclosure that performs the required operations is shown inFIG. 2.

EXAMPLES

Specific exemplary embodiments will now be further described by thefollowing, nonlimiting examples which will serve to illustrate in somedetail various features. The following examples are included tofacilitate an understanding of ways in which embodiments of the presentdisclosure may be practiced. However, it should be appreciated that manychanges can be made in the exemplary embodiments which are disclosedwhile still obtaining like or similar result without departing from thescope of embodiments of the present disclosure. Accordingly, theexamples should not be construed as limiting the scope of the presentdisclosure.

Example 1

Laser Predistortion Circuit For Dispersion-Slope Compensation

FIG. 2 is an example of the disclosure that demonstrates a laserpredistortion circuit including the signal path I(t) (the top path) anda predistortion path (bottom path). The predistortion path has greaterelectrical delay than the signal path since several operations(squaring, differentiating) are advantageously performed in this path.Therefore, a delay line (labeled “Delay 1”) is placed in the signal(top) path to ensure that both paths have the same delay. Delay linesare easily implemented; for example, it could be as simple as a lengthof coaxial cable and embodiments of this disclosure are not limited tospecific implementations.

In the predistortion (bottom) path, the box labeled “Squarer” 220squares the input current signal and the box labeled “d/dt” 230differentiates the input signal. There are a multitude of circuits thatperform these functions; the particular circuit implementation chosenwill be a tradeoff between cost and performance—the most important ofwhich is generation of the distortion terms while suppressing the(undesired) signal I and embodiments of this disclosure are not limitedto specific implementations.

An amplifier 210 (labeled “GAIN” in FIG. 2) provides the required gainfor the predistortion path. The variable attenuator 240 (labeled “ATTN”)is optional and can be implemented to ensure that the net gain due tothe amplifier and attenuator is the gain G_(opt) given by equation (3).The amplifier not only provides gain (or inverting gain if desired) butalso provides isolation between the two paths. The variable attenuatoris used to fine-tune for maximum suppression of the 2^(nd) orderdispersion-slope-induced distortions. The delay line labeled “Delay 2”in the predistortion path is optional and could be implemented if itmakes the task of equalizing the delay in the two paths easier.

The gain of the amplifier 210 would be set to the required value ofG_(opt) specified by equation (3) through software (such as a graphicaluser interface) in one of several ways: (1) the gain could bepre-programmed to a set value, (2) the gain could be manually entered bythe user, or (3) the user could enter the model number of the opticalcomponent and the software would choose the required gain by using alookup table.

Example 2

Adaptive Laser Predistortion Circuit For Dispersion-Slope Compensation

Another example of the disclosure that incorporates adaptivepredistortion is shown in FIG. 3. It is similar to the previous examplein that there is a direct path for the current signal (top path in FIG.3) and a predistortion path (middle path in FIG. 3) that generates thepredistortion current I_(predis) using a squarer 320, differentiator330, an RF amplifier 310 and an RF attenuator (not shown in FIG. 3).Rather than having to fine-tune an attenuator in order to obtain themaximum suppression of the 2^(nd) order dispersion-slope-induceddistortions as in the previous example, this example uses adaptivepredistortion to automatically adjust the amplifier 310 gain to obtainthe best degree of CSO suppression. This is done by using avoltage-controlled-amplifier (labeled “GAIN” in FIG. 3) whose gain canbe adjusted by an error voltage (labeled V_(err) in FIG. 3).

A 1×2 coupler 350 is placed after the optical component whosedistortions we are trying to suppress. A small part of the output of theoptical component is fed to a photodiode 360 and then a band-pass filter370 (labeled “BPF” in the lowest path in FIG. 3). The band-pass filteris tuned to a frequency where there is an unwanted second-orderdistortion present. For example, in a 1 GHz CATV system, if there is asignal present at 550 MHz, then any output at 1100 MHz would representan unwanted second-order distortion and hence the BPF would be tuned to1100 MHz. A gain control circuit 380 (“Gain Control” in FIG. 3) wouldamplify the output of the band-pass filter to yield the error voltageV_(err).

The gain of the amplifier (labeled “Gain” in FIG. 3) is set to thenominal value of G_(opt) given by equation (3). The gain of theamplifier is varied by the voltage V_(err) in such a fashion as tominimize the error voltage V_(err). There are many designs forvoltage-controlled-amplifiers that are controlled by an error voltageV_(err) where the gain is varied such as to minimize V_(err).

Minimizing the error voltage also results in minimization of thesecond-order distortions and embodiments of this disclosure are notlimited to specific designs.

Example 3

Another example of the adaptive predistortion technique where avoltage-controlled-attenuator is used rather than a voltage-controlledamplifier is shown in FIG. 4. As in the example shown in FIG. 3, anerror voltage V_(err) is derived by sampling a portion of the output ofthe optical component, detecting with a photodiode 460 and filteringwith a band-pass filter 470 tuned to a frequency where there is anunwanted second-order distortion. In this example, however, the errorvoltage V_(err) is used to control a voltage-controlled RF attenuator490 (labeled “VCA” in FIG. 4).The gain of the amplifier 410 (labeled“Gain” in FIG. 4) is set to the nominal value of G_(opt) given byequation (3). The attenuation of ATTN is varied by the voltage V_(err)in such a fashion as to minimize the error voltage V_(err). Thepredistortion paths include of a squarer 420, a differentiator 430, theRF amplifier 410 and the voltage-controlled RF attenuator 490.

The advantage of the examples described above that utilize adaptivepredistortion is that optimum suppression of dispersion-slope inducedCSO distortion is maintained even if the dispersion-slope of the opticalcomponent changes with time or laser parameters (such as the slopeS_(las) of the laser light-current characteristic) degrades with time.This ensures long-term stability of the predistortion technique. Anotherbenefit of using adaptive predistortion is that lookup tables containingthe properties of different models of optical components are no longerneeded—the same predistortion circuit provides optimum CSO suppressionfor different models of optical components that may have differentdispersion-slope values.

Example 4

Pre-Distortion Circuitry For Simultaneous and Independent Compensationof CSO Generated by Dispersion-Slope and Dispersion

CSO distortions can also be generated by the dispersion of opticalcomponents as well as the dispersion slope of such components. There aremany known techniques for compensating for the CSO distortion generatedby the dispersion of optical components, including laser predistortiontechniques. Therefore, laser predistortion techniques are known that canbe used to compensate for CSO distortions generated by the dispersion ofan optical component while the present disclosure describes a laserpredistortion technique that compensates for CSO distortions generatedby the dispersion-slope of an optical component.

It might seem that the two predistortion circuits could besimultaneously utilized in order to compensate for both the dispersionof one optical component and the dispersion-slope of a second opticalcomponent. (This does not preclude the case where the second opticalcomponent is the same as the first optical component.) This, however, isgenerally not the case. This is because the principle of superpositiondoes not apply due to the inherent nonlinearity of these circuits—thed/dt function is a linear function but the “squarer” is not linearcircuits (since it generates a current proportional to I²). Thus usingtwo compensation circuits, each of which compensate for one type ofdistortion, may end up not compensating for either type of distortionwhen combined. That is, the simultaneous use of both predistortioncircuitry would, in general, generate additional distortion terms thatwould degrade the effectiveness of both predistortion compensationtechniques or make it impossible to independently compensate for eachdistortion mechanism.

FIG. 5 shows a model relating the laser modulation current I(t), theoptical waveforms at the output of the laser 510 (P₁), the output of afirst optical component 520 (P₂), and the output of a second opticalcomponent 530 (P₃). It is assumed that second-order distortions aregenerated by the dispersion-slope S_(opt) of the first optical componentand by the dispersion D of the second optical component. For example,the second optical component could be a length of fiber, in which case Dwould represent the total fiber dispersion in units of ps/nm.

An analysis of the system described in FIG. 5 shows that the outputpower P₃ of the second optical component is given by the equation:

$\begin{matrix}{{P_{3}(t)} = {\alpha_{fib}\alpha_{opt}{{{P_{1}\left( {t - \tau_{fib} - \tau_{opt}} \right)}\left\lbrack {1 - \frac{\partial\tau_{fib}}{\partial t}} \right\rbrack}\left\lbrack {1 - \frac{\partial\tau_{opt}}{\partial t}} \right\rbrack}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$where α_(opt) and α_(fib) represent the optical loss of the first andsecond optical component, respectively, and τ_(opt), τ_(fib), representthe delay of the first and second optical component, respectively.

From this, further analysis shows that the CSO distortion at the outputof the receiver 540 generated by the combination of the dispersion-slopeof the first optical component and the dispersion of the second opticalcomponent is cancelled if the laser is modulated by a parallelcombination of I(t) and a predistortion current I_(preds)(t) given by:

$\begin{matrix}{{I_{predis} = {\left\lbrack {G_{fib} + G_{opt}} \right\rbrack\frac{\mathbb{d}\left( I^{2} \right)}{\mathbb{d}t}}}{where}} & \left( {{Equation}\mspace{14mu} 5} \right) \\{G_{fib} = {{- {{DL}\left( \frac{\lambda^{2}}{c} \right)}}\eta_{FM}}} & \left( {{Equation}\mspace{14mu} 6} \right) \\{G_{opt} = {\left( \frac{P_{0}S_{0}}{S_{1}} \right)\left( \frac{\lambda^{4}}{2\; c^{2}} \right)\eta_{FM}^{2}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$are the amplification factors required for the two types ofpredistortion (dispersion-slope of the first optical component anddispersion of the second optical component). The fact that G_(fib)depends only on the dispersion D of the second component and not thedispersion-slope of the first component, while G_(opt) depends only onthe dispersion-slope of the first optical component (and not on thedispersion of the second component) means that the dispersioncompensation and dispersion-slope compensation can be performedsimultaneously and independently.

FIG. 6 shows an example of the disclosure that provides for thesimultaneous, and independent, compensation of second-order distortionsgenerated by both the dispersion-slope of a first optical component andthe dispersion of a second optical component. It includes of a signalpath (top path) and two predistortion paths (bottom paths) fordispersion-slope compensation of a first optical component (bottom path)and dispersion compensation of a second optical component (middle path),respectively. Each of the predistortion paths include of a squarer 620,621, differentiator 630, 631, an RF amplifier 610, 611 and an RFattenuator 640, 641.

Each path has a simple delay line 650, 651 in order to equalize thedelays of the three paths. The predistortion path for dispersion-slopecompensation of a first optical component (bottom path) has a gainG_(opt) (given by equation 7) that is positive and proportional to thedispersion-slope of the first optical component. The predistortion pathfor dispersion compensation of a second optical component (middle path)has a gain G_(fib) (given by equation 6) that is negative andproportional to the dispersion of the second optical component. Therequired electrical gains are achieved through the use of an amplifierand attenuator in each of the two predistortion paths.

Note that the gain of the two predistortion paths are the negative ofeach other, reflecting the fact that the CSO distortions due todispersion and dispersion-slope are out of phase of each other.

Example 5

FIG. 7 shows another example of the disclosure that also provides forthe simultaneous, and independent, compensation of second-orderdistortions generated by both the dispersion-slope of a first opticalcomponent and the dispersion of a second optical component. In thisexample, the two predistortion paths of the previous example have beencombined into a single predistortion path. The predistortion pathincludes a squarer 720, differentiator 730, an RF amplifier 710 and anRF attenuator 740. The gain of the RF amplifier is now (G_(opt)+G_(fib))where G_(opt) is proportional to the dispersion-slope of the firstoptical component, and G_(fib) is proportional to the dispersion of thesecond optical component. This eliminates the need for one of the delaylines and simplifies the predistortion circuitry while still providingfor the simultaneous, and independent, compensation of dispersion anddispersion-slope.

Example 6

Other Equivalent Methods of Generating the Predistortion Currents.

The predistortion paths in all examples mentioned so far have employed asquarer and differentiator to realize a predistortion currentproportional to d(I²)/dt. There are many other equivalent methods ofrealizing a predistortion current proportional to d(I²)/dt. For example,using the identity d(I²)/dt=2 I (dI/dt), it is seen that d(I²)/dt can berealized by a differentiator and multiplier circuit (rather than adifferentiator and squarer) as illustrated in the example of thedisclosure shown in FIG. 8, as long as the gain of the amplifier isdoubled.

In this example, the predistortion path (lower path) includes of anamplifier 810, a differentiator 830, a multiplier 835, an attenuator 840and an optional delay line 850. The modulated current signal I(t) istapped off from the top path and multiplied with dI/dt at the multipliercircuit.

This is equivalent to the use of squarer and differentiator circuits.Many other circuit combinations are capable of generating the requiredpredistortion current proportional to d(I²)/dt and the embodiment ofthis disclosure are not limited to specific circuit combinations.

Example 7

Adaptive Compensation Circuitry in Optical Receiver For Simultaneous andIndependent Compensation of CSO Generated by Dispersion-Slope andDispersion

The compensation circuitry in all examples mentioned so far haveemployed the circuitry in (or coupled to) the optical transmitter. Sincethe generation of CSO distortion due to the dispersion anddispersion-slope of optical components is a linear process, thecompensation circuitry can be placed anywhere in the optical work—eitherin the optical transmitter prior to the light source or in the opticalreceiver after the optical photodiode.

FIG. 9 shows an example of the disclosure that provides for thesimultaneous, and independent, compensation of second-order distortionsgenerated by both the dispersion-slope of a first optical component andthe dispersion of a second optical component. In this example, thetwo-fold compensation circuitry is located in (or coupled to) theoptical receiver, rather than in the optical transmitter. Thecompensation circuitry includes of a primary direct path and a secondarypath including a squarer 920, differentiator 930, an RF amplifier 910and an RF attenuator 940. The gain of the RF amplifier is(G_(opt)+G_(fib)) where G_(opt) is proportional to the dispersion-slopeof a first optical component, and G_(fib) is proportional to thedispersion of a second optical component.

In order to obtain adaptive compensation, a portion of the output of thecompensation circuitry is fed to a band-pass filter 970 (labeled “BPF”in the lowest path in FIG. 9). The band-pass filter is tuned to afrequency where there is an unwanted second-order distortion present.For example, in a 1 GHz CATV system, if there is a signal present at 550MHz, then any output at 1100 MHz would represent an unwantedsecond-order distortion and hence the BPF would be tuned to 1100 MHz. Again control circuit (“Gain Control” in FIG. 9) would amplify the outputof the band-pass filter to yield the error voltage V_(err).

The gain of the amplifier (labeled “Gain” in FIG. 9) is set to thenominal value of (G_(opt)+G_(opt)) given by equations (6) and (7). Thegain of the amplifier is varied by the voltage V_(err) in such a fashionas to minimize the error voltage V_(err). There are many designs forvoltage-controlled-amplifiers that are controlled by an error voltageV_(err) where the gain is varied such as to minimize V_(err) and theembodiments of this disclosure are not limited to specific designs.Minimizing the error voltage also results in minimization of thesecond-order distortions.

CONCLUSION

Embodiments of this disclosure can include {1} a distortion compensationcircuit for compensation of the distortion generated by thedispersion-slope of an optical component and the frequency chirp of anoptical transmitter, where the distortion compensating circuit isincorporated into the optical transmitter, the optical receiver, or atsome intermediate point in a fiber-optic network; the distortioncompensation circuit comprising: a primary electrical signal path thatreceives at least a portion of the input signal and, optionally, a delayline; and a secondary signal path in parallel to the primary path thatreceives at least a portion of the input signal and including (notnecessarily in this order) of: an amplifier with an electrical currentgain that is proportional to the dispersion-slope of the opticalcomponent., an optional RF attenuator, an optional delay line, a“squarer” circuit whose output is the square of the input signal, and a“differentiator” circuit whose output is the derivative of the inputsignal (as shown in FIG. 2).

Embodiments of this disclosure can include the distortion compensationcircuit {1} (i.e. the sub-generic embodiment described by the precedingparagraph and identified by the tag “{1}”) wherein the “squarer” circuitin the secondary signal path is replaced by an equivalent “multiplier”circuit that multiplies a portion of the input signal (I) with itsderivative dI/dt (as shown in FIG. 8).

Embodiments of this disclosure can include the distortion compensationcircuit {1} wherein the compensation circuitry has been made “adaptive”by replacing the amplifier in the secondary signal path with avoltage-controlled amplifier and the addition of a feedback path thatreceives at least a portion of the signal at some point past the opticalcomponent that exhibits the dispersion-slope; the feedback pathcomprising: an optional photodiode (in case the portion of the signalthat is fed back is optical), a band-pass filter that is tuned to afrequency where there is an unwanted second-order distortion present,and a gain control circuit that amplifies the output of the band-passfilter to yield an error voltage that is used to control the gain of thevoltage-controlled amplifier in the secondary signal path (as shown inFIG. 3).

Embodiments of this disclosure can include the distortion compensationcircuit {1} wherein the compensation circuitry has been made “adaptive”by replacing the attenuator in the secondary path with avoltage-controlled attenuator and the addition of a feedback path thatreceives at least a portion of the signal at some point past the opticalcomponent that exhibits the dispersion-slope; the feedback pathcomprising: an optional photodiode (in case the portion of the signalthat is fed back is optical), a band-pass filter that is tuned to afrequency where there is an unwanted second-order distortion present,and a gain control circuit that amplifies the output of the band-passfilter to yield an error voltage that is used to control the attenuationof the voltage-controlled attenuator in the secondary path (as shown inFIG. 4).

Embodiments of this disclosure can include {5} a distortion compensationcircuit for simultaneous, and independent, compensation of second-orderdistortions generated by both the dispersion-slope of a first opticalcomponent and the dispersion of a second optical component, where thedistortion compensating circuit is incorporated into the opticaltransmitter, the optical receiver, or at some intermediate point in afiber-optic network; the distortion compensation circuit comprising: aprimary electrical signal path that receives at least a portion of theinput signal and, optionally, a delay line; and a secondary signal pathin parallel to the primary path that receives at least a portion of theinput signal and including (not necessarily in this order) of: anamplifier with an electrical current gain that is proportional to thedispersion-slope of the first optical component., an optional RFattenuator, an optional delay line, a “squarer” circuit whose output isthe square of the input signal, and a “differentiator” circuit whoseoutput is the derivative of the input signal; and a third signal path inparallel to the primary and secondary paths that receives at least aportion of the input signal and including (not necessarily in thisorder) of: an amplifier with an electrical current gain that isproportional to the dispersion of the second optical component., anoptional RF attenuator, an optional delay line, a “squarer” circuitwhose output is the square of the input signal, and a “differentiator”circuit whose output is the derivative of the input signal (as shown inFIG. 6).

Embodiments of this disclosure can include the distortion compensationcircuit {5} wherein the “squarer” circuits in the second and thirdsignal paths are replaced by equivalent “multiplier” circuits thatmultiplies a portion of the input signal (I) with its derivative dI/dt.

Embodiments of this disclosure can include the distortion compensationcircuit {5} wherein the compensation circuitry has been made “adaptive”by replacing the amplifiers in the second and third signal paths withvoltage-controlled amplifiers and the addition of a feedback path thatreceives at least a portion of the signal at some point past the opticalcomponent that exhibits the dispersion-slope; the feedback pathcomprising: an optional photodiode (in case the portion of the signalthat is fed back is optical), a band-pass filter that is tuned to afrequency where there is an unwanted second-order distortion present,and a gain control circuit that amplifies the output of the band-passfilter to yield an error voltage that is used to control the gains ofthe voltage-controlled amplifiers in the second and third signal paths.

Embodiments of this disclosure can include the distortion compensationcircuit {5} wherein the compensation circuitry has been made “adaptive”by replacing the attenuators in the second and third signal paths withvoltage-controlled attenuators and the addition of a feedback path thatreceives at least a portion of the signal at some point past the opticalcomponent that exhibits the dispersion-slope; the feedback pathcomprising: an optional photodiode (in case the portion of the signalthat is fed back is optical), a band-pass filter that is tuned to afrequency where there is an unwanted second-order distortion present,and a gain control circuit that amplifies the output of the band-passfilter to yield an error voltage that is used to control theattenuations of the voltage-controlled attenuators in the second andthird signal paths.

Embodiments of this disclosure can include a distortion compensationcircuit {9} for simultaneous, and independent, compensation ofsecond-order distortions generated by both the dispersion-slope of afirst optical component and the dispersion of a second opticalcomponent, where the distortion compensating circuit is incorporatedinto the optical transmitter, the optical receiver, or at someintermediate point in a fiber-optic network; the distortion compensationcircuit comprising: a primary electrical signal path that receives atleast a portion of the input signal and, optionally, a delay line; and asecondary signal path in parallel to the primary path that receives atleast a portion of the input signal and including (not necessarily inthis order) of: an amplifier with an electrical current gain equal to(G₁+G₂) where G₁ is proportional to the dispersion-slope of the firstoptical component, and G₂ is proportional to the dispersion of thesecond optical component, an optional RF attenuator, an optional delayline, a “squarer” circuit whose output is the square of the inputsignal, and a “differentiator” circuit whose output is the derivative ofthe input signal (as shown in FIG. 7).

Embodiments of this disclosure can include the distortion compensationcircuit {9} wherein the “squarer” circuit in the secondary signal pathis replaced by an equivalent “multiplier” circuit that multiplies aportion of the input signal (I) with its derivative dI/dt.

Embodiments of this disclosure can include the distortion compensationcircuit {9} wherein the compensation circuitry has been made “adaptive”by replacing the amplifier in the secondary signal path with avoltage-controlled amplifier and the addition of a feedback path thatreceives at least a portion of the signal at some point past the opticalcomponent that exhibits the dispersion-slope; the feedback pathcomprising: an optional photodiode (in case the portion of the signalthat is fed back is optical), a band-pass filter that is tuned to afrequency where there is an unwanted second-order distortion present,and a gain control circuit that amplifies the output of the band-passfilter to yield an error voltage that is used to control the gain of thevoltage-controlled amplifier in the secondary signal path.

Embodiments of this disclosure can include the distortion compensationcircuit {9} wherein the compensation circuitry has been made “adaptive”by replacing the attenuator in the secondary signal path with avoltage-controlled attenuator and the addition of a feedback path thatreceives at least a portion of the signal at some point past the opticalcomponent that exhibits the dispersion-slope; the feedback pathcomprising: an optional photodiode (in case the portion of the signalthat is fed back is optical), a band-pass filter that is tuned to afrequency where there is an unwanted second-order distortion present,and a gain control circuit that amplifies the output of the band-passfilter to yield an error voltage that is used to control the attenuationof the voltage-controlled attenuator in the secondary signal path.

The terms program and software and/or the phrases program elements,computer program and computer software are intended to mean a sequenceof instructions designed for execution on a computer system (e.g., aprogram and/or computer program, may include a subroutine, a function, aprocedure, an object method, an object implementation, an executableapplication, an applet, a servlet, a source code, an object code, ashared library/dynamic load library and/or other sequence ofinstructions designed for execution on a computer or computer system).The phrase radio frequency (RF) is intended to mean frequencies lessthan or equal to approximately 300 GHz as well as the infrared spectrum.The term light is intended to mean frequencies greater than or equal toapproximately 300 GHz as well as the microwave spectrum.

The term uniformly is intended to mean unvarying or deviate very littlefrom a given and/or expected value (e.g, within 10% of). The termsubstantially is intended to mean largely but not necessarily whollythat which is specified. The term approximately is intended to mean atleast close to a given value (e.g., within 10% of). The term generallyis intended to mean at least approaching a given state. The term coupledis intended to mean connected, although not necessarily directly, andnot necessarily mechanically.

The terms first or one, and the phrases at least a first or at leastone, are intended to mean the singular or the plural unless it is clearfrom the intrinsic text of this document that it is meant otherwise. Theterms second or another, and the phrases at least a second or at leastanother, are intended to mean the singular or the plural unless it isclear from the intrinsic text of this document that it is meantotherwise. Unless expressly stated to the contrary in the intrinsic textof this document, the term or is intended to mean an inclusive or andnot an exclusive or. Specifically, a condition A or B is satisfied byany one of the following: A is true (or present) and B is false (or notpresent), A is false (or not present) and B is true (or present), andboth A and B are true (or present). The terms a and/or an are employedfor grammatical style and merely for convenience.

The term plurality is intended to mean two or more than two. The termany is intended to mean all applicable members of a set or at least asubset of all applicable members of the set. The phrase any integerderivable therein is intended to mean an integer between thecorresponding numbers recited in the specification. The phrase any rangederivable therein is intended to mean any range within suchcorresponding numbers. The term means, when followed by the term “for”is intended to mean hardware, firmware and/or software for achieving aresult. The term step, when followed by the term “for” is intended tomean a (sub)method, (sub)process and/or (sub)routine for achieving therecited result. Unless otherwise defined, all technical and scientificterms used herein have the same meaning as commonly understood by one ofordinary skill in the art to which this present disclosure belongs. Incase of conflict, the present specification, including definitions, willcontrol.

The described embodiments and examples are illustrative only and notintended to be limiting. Although embodiments of the present disclosurecan be implemented separately, embodiments of the present disclosure maybe integrated into the system(s) with which they are associated. All theembodiments of the present disclosure disclosed herein can be made andused without undue experimentation in light of the disclosure.Embodiments of the present disclosure are not limited by theoreticalstatements (if any) recited herein. The individual steps of embodimentsof the present disclosure need not be performed in the disclosed manner,or combined in the disclosed sequences, but may be performed in any andall manner and/or combined in any and all sequences. The individualcomponents of embodiments of the present disclosure need not be combinedin the disclosed configurations, but could be combined in any and allconfigurations.

Various substitutions, modifications, additions and/or rearrangements ofthe features of embodiments of the present disclosure may be madewithout deviating from the scope of the underlying inventive concept.All the disclosed elements and features of each disclosed embodiment canbe combined with, or substituted for, the disclosed elements andfeatures of every other disclosed embodiment except where such elementsor features are mutually exclusive. The scope of the underlyinginventive concept as defined by the appended claims and theirequivalents cover all such substitutions, modifications, additionsand/or rearrangements.

The appended claims are not to be interpreted as includingmeans-plus-function limitations, unless such a limitation is explicitlyrecited in a given claim using the phrase(s) “means for” or “mechanismfor” or “step for”. Sub-generic embodiments of this disclosure aredelineated by the appended independent claims and their equivalents.Specific embodiments of this disclosure are differentiated by theappended dependent claims and their equivalents.

What is claimed is:
 1. An apparatus, comprising a distortioncompensation circuit to substantially cancel composite second orderdistortion generated by at least 1) a dispersion-slope of an opticalcomponent and 2) frequency chirp of an optical transmitter, thedistortion compensation circuit including a 1×n electrical coupler; aprimary signal path including an RF delay line coupled to the 1×ncoupler, the primary signal path receiving a first portion of an inputsignal; a n×1 electrical coupler coupled to the primary signal path; anda secondary signal path coupled to both i) the 1×n coupler and ii) then×1 coupler and in parallel to the primary signal path, the secondarysignal path receiving a second portion of the input signal and includingan RF delay line, an RF attenuator, an amplifier with electrical currentgain proportional to the dispersion-slope of the optical component, acircuit that squares the signal current and a circuit whose output is aderivative of its input signal.
 2. The apparatus of claim 1, furthercomprising an optical transmitter that follows the distortioncompensation circuit by an electrical connection to the n×1 coupler ofthe compensation circuit.
 3. The apparatus of claim 1, furthercomprising an optical receiver that precedes the distortion compensationcircuit by an electrical input coupled to the 1×n coupler of thecompensation circuit.
 4. The apparatus of claim 1, wherein the amplifierhas electrical current gain proportional to both the dispersion-slope ofthe optical component and the dispersion of another optical component.5. A fiber optic network comprising the apparatus of claim 1.